Questions tagged [kerr-metric]
The Kerr metric describes the geometry of empty spacetime around a rotating uncharged axially-symmetric black hole.
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Condition on conserved quantities to escape Kerr black hole
For a classical two-body gravitational system, we can easily check whether the trajectory is bounded by calculating the energy. If the energy is larger than a threshold $E > E_0$ (and if they are ...
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What is the difference between Innermost Bound Circular Orbit (IBCO), Innermost Bound Spherical Orbit (IBSO), and Sphere Radius?
⚠ My question is related to Schwartzchild and Kerr Blackholes.
In a few words:
Innermost Bound Circular Orbit (IBCO):
It is the constant radius at which this circular orbit occurs at 1.5 Schwarzchild ...
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Interpretation of geodesics in Kerr metric when approaching the event horizon
I'm learning about the Kerr metric and Kerr black holes from the book "General Relativity: An Introduction for Physicists, M.P.Hobson" and I'm interested in an interpretation for the ...
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Can we be alive in spinning Black Holes? [duplicate]
I was studying about black holes and I get to know that we can be alive in black holes if the black hole is spinning. I didn't understand the reason. Can anyone explain.
I mean to ask that if is it ...
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Kerr metric in Boyer-Lindquist-isotropic form?
The non-zero elements of the Kerr metric in advanced Eddington-Finkelstein starting from the Schwarzschild metric in isotropic coordinates is
\begin{equation}
\begin{split}
g_{u\varphi} = ...
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Why are complex coordinates outlawed in physics?
In the case of the Kerr metric, for a high enough angular velocity such that on transformation to Boyer-Lindquist coordinates yields complex coordinates for the event horizon, why is it assumed then ...
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Is a black hole spherical?
Black holes are usually created when massive stars use up all their fuel and collapse due to gravitational collapse.
All stars rotate.
However, since angular momentum must be conserved even when they ...
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Exact meaning of the mass $M$ in the Kerr metric event horizon?
Posting this as I have so far not been able to find a straightforward answer to the following question. The formula for the outer event horizon of a kerr black hole is given by the following equation:
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What is Kerr doing here?
On pages 19-20 of Kerr's conference about how he discovered his metric, he basically performs several coordinate transformations until reaching:
$$ds^2 = dx^2 + dy^2 + dz^2 - dt^2 + \dfrac{2mr^3}{r^4 +...
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Why does $a\cos{\theta}$ represent rotation in the Kerr metric?
In any introductory book to GR where the Kerr metric is reviewed, they all apply transformations of the form:
$$cu' = cu + ia\cos\theta;\text{ } r' = r + ia\cos\theta$$
In the end, the result ...
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How to derive Smarr formula for Kerr Black Hole?
Following is the Smarr formula for Kerr Black Hole
$$M=\frac{\kappa A}{4\pi}+2 \Omega J $$
where $\kappa, \Omega$, $J$ and $A$ are surface gravity, angular velocity, angular momentum and surface area ...
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Quantum field expansion and bogoliubov coefficients in the interior of a rotating black hole
I am trying to quantize a real scalar field in the interior of a rotating black hole (3+1 D, asymptotically flat). My question is regarding the modes of the radial part of the equation (obtained after ...
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How does loop quantum gravity handle spacetimes which aren't globally hyperbolic, like the Kerr metric?
Loop quantum gravity assumes spacetime is globally hyperbolic. However, the interior of a Kerr black hole isn't globally hyperbolic, containing closed timelike curves. So, how are Kerr black holes ...
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Checking inverse metric and Christoffel symbols for the Kerr metric against references
I am trying to cross-check the Christoffel symbols and other very laborious geometric components in several metrics. In particular the Kerr metric is notoriously complex and results in expressions ...
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Can a Kerr black hole become super-extremal?
Let's assume there is a large Kerr black hole, which is almost
extremal and would become extremal with the addition of a small
amount of mass $M$ with spin $J$ to make the final $J=M$.
What if this ...
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What happens to the ring singularities when two Kerr black holes merge?
Imagine two Kerr black holes with ring singularities oriented in different axes (e.g. one horizontal and the other one vertical). If they merge, what will happen to these singularities? Will they form ...
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What are spinning black holes orbiting?
I have seen depictions of spinning black holes with the "singularity" spinning around a center of rotation in a flat plane, or moving around an imaginary sphere. Is there anything in the ...
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Is the Schwarzschild singularity a limit of the Kerr singularity?
In a Schwarzschild black hole, the singularity is spacelike. In a Kerr black hole, it is timelike.
Is there any continuous transformation between those solutions? Can the Schwarzschild solution be ...
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Why domain of Kerr black hole includes negative values for $r$ coordinate?
I understand the domain of $t$ is all real numbers but mathematically, how to prove the domain of $r$ coordinate is also all real numbers except $r=0$ when $\theta = \pi/2$. I know that we get two ...
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Does someone falling into a spinning black hole see the end of the universe?
It is well known that if you fall into the Schwarzschild black hole you cannot see the entirety of the outside spacetime since there are photons which cannot catch up with you before you reach the ...
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Angular velocity of stationary observer
I am studying Kerr metric in Boyer Lindquist coordinates and having trouble in understanding the components of angular velocity of stationary observer with constant r and $\theta$ motion w.r.t ...
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Significance of simultaneous transformation of $t$ and $\phi$ in kerr metric
The Kerr metric in Boyer-Lindquist coordinate is invariant under simultaneous transformations $t \rightarrow -t$ and $\phi \rightarrow -\phi$ but not invariant if we apply one transformation only. ...
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Perimeter of Kerr's event horizon
We can compute the "proper circumference" of the Schwarzschild event horizon integrating its line element along its perimeter at a fixed $t$. This would be the minimum length of a rope that ...
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Is it possible to refind entry trajectory after leaving a rotating black hole?
I'm asking about the case where an infalling object travels a path right through a rotating black hole, intact.
I want to provide a simple parallel for the purposes of question clarity:
A horse can ...
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What actually is Boyer-Lindquist coordinates?
I want to know the difference between spherical and Boyer-Lindquist coordinates. Don't they both use $r, \theta, \phi$ parameters? I've searched books and sources on the internet and there's none that ...
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Gray body factors of PBH's - radial equation approximation (Page 1976)
I'm deriving the results of the Page paper: "Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole*" (https://doi.org/10.1103/PhysRevD.13.198). At ...
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What happens if $ a^2 > M^2 $ in Kerr metric?
(Boyer-Lindquist coordinates and $ c = G =1 $ taken)
As I know, line element in Kerr metric $ d s^2 = - \left( 1 - \frac{2Mr}{\rho^2} \right) d t^2 - \frac{4 M a r \sin^2 \theta}{\rho^2} d \phi d t + \...
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Is it possible that black holes spin in discreet spin quanta?
Roy Kerr recently wrote a paper critical of the Penrose singularity theorem. One interpretation of his paper is that the singularity problem might be an artifact of the Schwarzchild metric and that a ...
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The Kerr metric applied to a solid rotating body
Can the Kerr metric be used as an exterior solution to analyse the vacuum outside a rotating solid body or does it only apply to a rotating black hole? If it can't, is there an alternative exterior ...
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Calculating the determinant of the Kerr metric
I have been trying to calculate the determinant of the Kerr metric (described by equation 11.71, A First Course in General Relativity: 3rd Edition, B. Schutz):
$$\begin{align}ds^2 &=-\frac{(\Delta-...
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Finding the Four-Velocity vector in the Kerr spacetime between two points?
For over a year me and a friend have been working on a Kerr Black Hole renderer. We are close to the finish line and get renders like these;
These renders show aberration of light due to the cameras ...
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Causality violation in Kerr metric
my professor told me that in Kerr metric, there is a zone of causality violation around the ring singularity, but he was saying this in the context of $M^2>a^2$, does this also apply to the cases ...
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Question on the transformation from Boyer-Lindquist to Kerr-Schild coordinates, for a modified Kerr metric
From Kerr metric, we do know that there exist a function with the form of:
$$\Delta = r^2 - 2 M r + a^2 \tag{1}.$$
Following $[1]$, I did understand the coordinate transformation from Boyer-Lindquist (...
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Hawking radiation from photons?
I am reading a lot of papers that derive the Hawking temperature solving either the Klein Gordon equation for scalar fields or the Dirac equation for spin $\tfrac12$ particles via tunnelling ...
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Question about Kerr's recent paper regarding Penrose et al.'s works on gravitational singularities [duplicate]
R. Kerr posted an essay on arxiv recently.
Kerr claims:
The consensus view for sixty years has been that all black holes have singularities. There is no direct proof of this, only the papers by ...
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Is it possible for an object on an initially retrograde orbit to pass through the ergosphere or a rotating black hole and emerge?
I say "initially retrograde" because am aware that while inside the ergosphere, everything necessarily has prograde motion. So the two options I can envision are:
The object approaches the ...
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What metric can describe best the spacetime outside a rotating star?
I hope this question is not mistreated as a duplicate, because that is not my intention.
The Kerr metric suffices to describe the exterior solution to an axisymmetric spacetime mass distribution of ...
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Asymptotic development of the black-hole metric
In the Kruskal-Szekeres extension of the Schwarzschild metric parallel universes appear. In a couple of questions on this site, for instance: Where does the parallel universe in the Penrose diagram ...
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Why does Roy Kerr claim that the Kerr black hole does not contain a singularity?
In a preprint posted on the arXiv, Roy Kerr claims that there is a widespread misunderstanding related to the singularity inside the black hole that bears his name.
Can anyone explain his argument in ...
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Redshift near Kerr Black Hole
The question is related to Sean Carroll's Spacetime and Geometry ex 6.6.
Consider a Kerr black hole with an accretion disk of negligible mass. Particles in the disk follow geodesics. Some iron in the ...
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Schwarzschild and Kerr solution in $(x, y, z, t)$ coordinates?
The Schwarzschild solution ('simple' black holes) and the Kerr solution (rotating black holes) are very well known in General Relativity.
The coordinates which are used to describe them are mostly ...
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Rotating Black Holes and Birkhoff's theorem
I found a few questions that are similar to mine, but I do not think that either of them answers exactly what I want:
Is there a Birkhoff-like theorem for stationary axisymmetric metrics?
or
...
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Coordinate transform of Kerr metric to Kerr-Schild coordinates
the transformation from Boyer-Lindquist $\{t,r,\theta,\phi\}$ coordinates to Kerr-Schild $\{t',r,\theta,\phi' \}$coordinates can be written as
$$
dt' = dt + \frac{2 M r}{r^2 - 2 M r + a^2} dr, \;\;\; ...
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How to describe the four-current of a tilted loop in Kerr spacetime
consider the Kerr metric in Boyer-Lindquist coordinates.
We usually describe the source of an electromagnetic field by the four vector $J^\mu$.
$$J^\mu = \{\rho, j^1, j^2, j^3\}.$$
Now we have an ...
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Is there a distance at which the Kerr metric looks like the Schwarzschild metric?
As the title says: Is there a distance at which the Kerr metric looks like Schwarzschild metric?
Edit: if there isn't any such distance (smaller than infinity), can we measure from the outside, with ...
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Spheroidal eigenvalues with shifted boundary conditions
I was studying the spheroidal differential equation in relation to calculating solutions for fields in a general Kerr background metric and, as far as I can tell, the eigenvalues $\lambda$ that enter ...
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What vacuum should be defined for a observer in Kerr spacetime?
A scalar field in Kerr spacetime can have two kinds of modes, one labeled by "in", and the other by "up". The "in" modes originate from the past null infinity, while the &...
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Carter Constant with a Cosmological Constant
The Carter constant for the Kerr Newman metric
$$ \rm C = p_{\theta}^{2} + \cos^{2}\theta \ \Bigg[ a^2 \ (m^2 - E^2) + \left(\frac{L_z}{\sin\theta} \right)^{2} \Bigg] $$
with (in $[+---]$ signature)
$$...
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What are the effects on a stationary observer at a specific distance from a Kerr Black Hole?
A Kerr Black Hole (BH) is a spinning BH. There is an Event Horizon (EH) which is
$$r_H^\pm =\frac{r_{S} \pm \sqrt{r_{S}^2 - 4a^2}}{2},$$
where $a = \frac{J}{Mc}$ and $r_{S}$ is the Schwarzschild ...
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